I use Mylyn 3.0.4 with MyEclipse 7.0 against a JIRA repository. I think
ever since MyEclipse 7.0, the "Open with Web Browser" button on the JIRA
bug in Eclipse doesn't work anymore - nothing happens when I press it (the
button has a "pressed animation", though).

I have Eclipse configured to use the internal web browser. But even when
I open both the internal web browser and the MyEclipse browser, the bug
still doesn't show up in either of the two.